The academics believe those who suffer cognitive decline – leaving them less sharp in old age – may be more prone to dementia.

There is already evidence that having more than seven hours of sleep a night can lead to weight gain and increase the risk of heart problems and diabetes. However, the new study is one of the first to link it to concentration problems.

The research, presented at the Alzheimer’s Association International Conference in Vancouver, Canada, looked at 15,000 women in their seventies over five years.

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The participants all underwent regular tests to check their memory, concentration and attention span – and those who usually slept for seven hours performed far better than those who got less than five hours, or more than nine.

Lead researcher Elizabeth Devore of Brigham and Women’s Hospital, Boston, said: ‘Our findings support the notion that extreme sleep durations and changes in sleep duration over time may contribute to cognitive decline and early Alzheimer’s changes in older adults.

‘The public health implications of these findings could be substantial, as they might lead to the eventual identification of sleep-based strategies for reducing risk of cognitive impairment and Alzheimer’s.’

Quality and duration: Too much, or too little sleep could be bad for your brain

A spokesman for the Alzheimer’s Society added: ‘A good night’s sleep is one of life’s pleasures but, once again, this robust research suggests that the quality and duration of sleep are also linked to our cognitive health.

‘While this link is now quite well-established, more research is needed to determine whether factors like sleep duration are a cause or effect of cognitive decline.

‘We’re not saying you shouldn’t enjoy the occasional lie-in, but good-quality sleep, eating a balanced diet, maintaining a healthy weight and exercising regularly can all make a difference in reducing your risk.’

Another study presented at the conference found that women who have breathing problems when they sleep had a higher risk of dementia. Sufferers of sleep apnoea – who suddenly stop breathing at night – were more than twice as likely to develop the condition.

The researchers from the University of California, San Francisco looked at 1,300 women in their late seventies.

Lead scientist Kristine Yaffe said: ‘We believe that these results indicate that the relationship between sleep-disordered breathing and dementia may be connected to the decrease in oxygen associated with sleep apnoea and not to disrupted patterns of sleep.'